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108
Predicate Encryption Supporting Disjunctions, Polynomial Equations, and Inner Products
"... Abstract. Predicate encryption is a new paradigm generalizing, among other things, identitybased encryption. In a predicate encryption scheme, secret keys correspond to predicates and ciphertexts are associated with attributes; the secret key SKf corresponding to a predicate f can be used to decryp ..."
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Cited by 168 (23 self)
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Abstract. Predicate encryption is a new paradigm generalizing, among other things, identitybased encryption. In a predicate encryption scheme, secret keys correspond to predicates and ciphertexts are associated with attributes; the secret key SKf corresponding to a predicate f can be used to decrypt a ciphertext associated with attribute I if and only if f(I) = 1. Constructions of such schemes are currently known for relatively few classes of predicates. We construct such a scheme for predicates corresponding to the evaluation of inner products over ZN (for some large integer N). This, in turn, enables constructions in which predicates correspond to the evaluation of disjunctions, polynomials, CNF/DNF formulae, or threshold predicates (among others). Besides serving as a significant step forward in the theory of predicate encryption, our results lead to a number of applications that are interesting in their own right. 1
How to delegate and verify in public: Verifiable computation from attributebased encryption
 In Proceedings of the 9th Theory of Cryptography Conference, TCC ’12
, 2012
"... Abstract. The wide variety of small, computationally weak devices, and the growing number of computationally intensive tasks makes it appealing to delegate computation to data centers. However, outsourcing computation is useful only when the returned result can be trusted, which makes verifiable com ..."
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Cited by 55 (6 self)
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Abstract. The wide variety of small, computationally weak devices, and the growing number of computationally intensive tasks makes it appealing to delegate computation to data centers. However, outsourcing computation is useful only when the returned result can be trusted, which makes verifiable computation (VC) a must for such scenarios. In this work we extend the definition of verifiable computation in two important directions: public delegation and public verifiability, which have important applications in many practical delegation scenarios. Yet, existing VC constructions based on standard cryptographic assumptions fail to achieve these properties. As the primary contribution of our work, we establish an important (and somewhat surprising) connection between verifiable computation and attributebased encryption (ABE), a primitive that has been widely studied. Namely, we show how to construct a VC scheme with public delegation and public verifiability from any ABE scheme. The VC scheme verifies any function in the class of functions covered by the permissible ABE policies (currently Boolean formulas). This scheme enjoys a very efficient verification algorithm that depends only on the output size. Efficient delegation, however, requires the ABE encryption algorithm to be cheaper than the original function computation. Strengthening this connection, we show a construction of a multifunction verifiable computation scheme from an ABE scheme with outsourced decryption, a primitive defined recently by Green, Hohenberger and Waters (USENIX Security 2011). A multifunction VC scheme allows the verifiable evaluation of multiple functions on the same preprocessed input. In the other direction, we also explore the construction of an ABE scheme from verifiable computation protocols.
Attributebased encryption for circuits from multilinear maps. Cryptology ePrint Archive, Report 2013/128, 2013. http://eprint.iacr.org/. Oded Goldreich and
"... In this work, we provide the first construction of AttributeBased Encryption (ABE) for general circuits. Our construction is based on the existence of multilinear maps. We prove selective security of our scheme in the standard model under the natural multilinear generalization of the BDDH assumptio ..."
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Cited by 54 (8 self)
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In this work, we provide the first construction of AttributeBased Encryption (ABE) for general circuits. Our construction is based on the existence of multilinear maps. We prove selective security of our scheme in the standard model under the natural multilinear generalization of the BDDH assumption. Our scheme achieves both KeyPolicy and CiphertextPolicy variants of ABE. Our scheme and its proof of security directly translate to the recent multilinear map framework of Garg, Gentry, and Halevi. This paper subsumes the manuscript of Sahai and Waters [SW12].
Reusable garbled circuits and succinct functional encryption
, 2013
"... Garbled circuits, introduced by Yao in the mid 80s, allow computing a function f on an input x without leaking anything about f or x besides f(x). Garbled circuits found numerous applications, but every known construction suffers from one limitation: it offers no security if used on multiple inputs ..."
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Cited by 42 (3 self)
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Garbled circuits, introduced by Yao in the mid 80s, allow computing a function f on an input x without leaking anything about f or x besides f(x). Garbled circuits found numerous applications, but every known construction suffers from one limitation: it offers no security if used on multiple inputs x. In this paper, we construct for the first time reusable garbled circuits. The key building block is a new succinct singlekey functional encryption scheme. Functional encryption is an ambitious primitive: given an encryption Enc(x) of a value x, and a secret key skf for a function f, anyone can compute f(x) without learning any other information about x. We construct, for the first time, a succinct functional encryption scheme for any polynomialtime function f where succinctness means that the ciphertext size does not grow with the size of the circuit for f, but only with its depth. The security of our construction is based on the intractability of the Learning with Errors (LWE) problem and holds as long as an adversary has access to a single key skf (or even an a priori bounded number of keys for different functions). Building on our succinct singlekey functional encryption scheme, we show several new applications in addition to reusable garbled circuits, such as a paradigm for general function obfuscation which we call tokenbased obfuscation, homomorphic encryption for a class of Turing machines where the evaluation runs in inputspecific time rather than worstcase time, and a scheme for delegating computation which is publicly verifiable and maintains the privacy of the computation.
Attributebased encryption for circuits
 In STOC
"... In an attributebased encryption (ABE) scheme, a ciphertext is associated with an ℓbit public index ind and a message m, and a secret key is associated with a Boolean predicate P. The secret key allows to decrypt the ciphertext and learn m iff P (ind) = 1. Moreover, the scheme should be secure aga ..."
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Cited by 42 (11 self)
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In an attributebased encryption (ABE) scheme, a ciphertext is associated with an ℓbit public index ind and a message m, and a secret key is associated with a Boolean predicate P. The secret key allows to decrypt the ciphertext and learn m iff P (ind) = 1. Moreover, the scheme should be secure against collusions of users, namely, given secret keys for polynomially many predicates, an adversary learns nothing about the message if none of the secret keys can individually decrypt the ciphertext. We present attributebased encryption schemes for circuits of any arbitrary polynomial size, where the public parameters and the ciphertext grow linearly with the depth of the circuit. Our construction is secure under the standard learning with errors (LWE) assumption. Previous constructions of attributebased encryption were for Boolean formulas, captured by the complexity class NC1. In the course of our construction, we present a new framework for constructing ABE schemes. As a byproduct of our framework, we obtain ABE schemes for polynomialsize branching programs, corresponding to the complexity class LOGSPACE, under quantitatively better assumptions.
Functional Encryption with Bounded Collusions via MultiParty Computation ∗
, 2012
"... We construct a functional encryption scheme secure against an apriori bounded polynomial number of collusions for the class of all polynomialsize circuits. Our constructions require only semantically secure publickey encryption schemes and pseudorandom generators computable by smalldepth circuit ..."
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Cited by 38 (8 self)
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We construct a functional encryption scheme secure against an apriori bounded polynomial number of collusions for the class of all polynomialsize circuits. Our constructions require only semantically secure publickey encryption schemes and pseudorandom generators computable by smalldepth circuits (known to be implied by most concrete intractability assumptions). For certain special cases such as predicate encryption schemes with public index, the construction requires only semantically secure encryption schemes, which is clearly the minimal necessary assumption. Our constructions rely heavily on techniques from secure multiparty computation and randomized encodings. All our constructions are secure under a strong, adaptive simulationbased definition of functional encryption.
Functional Encryption for Inner Product Predicates from Learning with Errors
, 2011
"... We propose a latticebased functional encryption scheme for inner product predicates whose security follows from the difficulty of the learning with errors (LWE) problem. This construction allows us to achieve applications such as range and subset queries, polynomial evaluation, and CNF/DNF formulas ..."
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Cited by 38 (12 self)
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We propose a latticebased functional encryption scheme for inner product predicates whose security follows from the difficulty of the learning with errors (LWE) problem. This construction allows us to achieve applications such as range and subset queries, polynomial evaluation, and CNF/DNF formulas on encrypted data. Our scheme supports inner products over small fields, in contrast to earlier works based on bilinear maps. Our construction is the first functional encryption scheme based on lattice techniques that goes beyond basic identitybased encryption. The main technique in our scheme is a novel twist to the identitybased encryption scheme of Agrawal, Boneh and Boyen (Eurocrypt 2010). Our scheme is weakly attribute hiding in the standard model.
Fully Secure Functional Encryption without Obfuscation
"... Previously known functional encryption (FE) schemes for general circuits relied on indistinguishability obfuscation, which in turn either relies on an exponential number of assumptions (basically, one per circuit), or a polynomial set of assumptions, but with an exponential loss in the security red ..."
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Cited by 29 (3 self)
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Previously known functional encryption (FE) schemes for general circuits relied on indistinguishability obfuscation, which in turn either relies on an exponential number of assumptions (basically, one per circuit), or a polynomial set of assumptions, but with an exponential loss in the security reduction. Additionally these schemes are proved in an unrealistic selective security model, where the adversary is forced to specify its target before seeing the public parameters. For these constructions, full security can be obtained but at the cost of an exponential loss in the security reduction. In this work, we overcome the above limitations and realize a fully secure functional encryption scheme without using indistinguishability obfuscation. Specifically the security of our scheme relies only on the polynomial hardness of simple assumptions on multilinear maps. 1
Outsourcing the decryption of abe ciphertexts
 In Proceedings of the USENIX Security Symposium
, 2011
"... Attributebased encryption (ABE) is a new vision for public key encryption that allows users to encrypt and decrypt messages based on user attributes. For example, a user can create a ciphertext that can be decrypted only by other users with attributes satisfying (“Faculty ” OR (“PhD Student ” AND “ ..."
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Cited by 29 (2 self)
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Attributebased encryption (ABE) is a new vision for public key encryption that allows users to encrypt and decrypt messages based on user attributes. For example, a user can create a ciphertext that can be decrypted only by other users with attributes satisfying (“Faculty ” OR (“PhD Student ” AND “Quals Completed”)). Given its expressiveness, ABE is currently being considered for many cloud storage and computing applications. However, one of the main efficiency drawbacks of ABE is that the size of the ciphertext and the time required to decrypt it grows with the complexity of the access formula. In this work, we propose a new paradigm for ABE that largely eliminates this overhead for users. Suppose that ABE ciphertexts are stored in the cloud. We show how a user can provide the cloud with a single transformation key that allows the cloud to translate any ABE ciphertext satisfied by that user’s attributes into a (constantsize) El Gamalstyle ciphertext, without the cloud being able to read any part of the user’s messages. To precisely define and demonstrate the advantages of this approach, we provide new security definitions for both CPA and replayable CCA security with outsourcing, several new constructions, an implementation of our algorithms and detailed performance measurements. In a typical configuration, the user saves significantly on both bandwidth and decryption time, without increasing the number of transmissions.
Functional encryption for regular languages
 In CRYPTO
, 2012
"... We provide a functional encryption system that supports functionality for regular languages. In our system a secret key is associated with a Deterministic Finite Automata (DFA) M. A ciphertext CT encrypts a message m and is associated with an arbitrary length string w. A user is able to decrypt the ..."
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Cited by 21 (0 self)
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We provide a functional encryption system that supports functionality for regular languages. In our system a secret key is associated with a Deterministic Finite Automata (DFA) M. A ciphertext CT encrypts a message m and is associated with an arbitrary length string w. A user is able to decrypt the ciphertext CT if and only if the DFA M associated with his private key accepts the string w. Compared with other known functional encryption systems, this is the first system where the functionality is capable of recognizing an unbounded language. For example, in (KeyPolicy) AttributeBased Encryption (ABE) a private key SK is associated with a single boolean formula φ which operates over a fixed number of boolean variables from the ciphertext. In contrast, in our system a DFA M will meaningfully operate over an arbitrary length input w. We propose a system that utilizes bilinear groups. Our solution is a “public index ” system, where the message m is hidden, but the string w is not. We prove security in the selective model under a variant of the decision ℓBilinear DiffieHellman Exponent (BDHE) assumption that we call the decision ℓExpanded BDHE problem. 1